What is the integral of (tan(x))/(cos(x)) ?

The integral of (tan(x))/(cos(x)) is sec(x)+C

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integral of (tan(x))/(cos(x))

\int \frac{tan ( x )}{cos ( x )} d x

sec (x) + C

Solution steps

\int \frac{tan ( x )}{cos ( x )} d x

Rewrite using trig identities

= \int tan (x) sec (x) d x

Apply u-substitution

: \int 1 d u

= \int 1 d u

Integral of a constant:

\int a d x = a x

= 1 \cdot u

Substitute back

u = sec (x)

= 1 \cdot sec (x)

Simplify

= sec (x)

Add a constant to the solution

= sec (x) + C

x \to 4 lim (9 \cdot 27)

x \to - 1 lim (x - ln (- x - 1))

arctan (\frac{y}{x})

\int_{0}^{3} ∣ 3 x - 5 ∣ d x

\frac{d}{d x} (1 - \frac{3 x}{x ^{3} + 27})

What is the integral of (tan(x))/(cos(x)) ?
The integral of (tan(x))/(cos(x)) is sec(x)+C